**5. Simulation Results**

To study the performance of the proposed controller, the small power system is considered as shown in Figure 6. The model of the wind turbine considered in this paper is defined as type-4, where the WT is connected to the grid through a full rated back-to-back converter. The machine used in this system is based on a permanent magne<sup>t</sup> synchronous generator (PMSG). The machine side converter is controlled to extract the desired power from the wind. The active and reactive power is controlled using the grid-side inverter. The detailed model of the implemented WT system and its designed controller are presented in reference [51].

In the first study, one single WES was used to test the performance of the fuzzy logic-based controller. Different static droop curves were tested and compared with the proposed approach. The WES was set to regulate the frequency of the grid by providing the required power. The loads in the power system are supplied by the synchronous generator and the WES. The conventional synchronous generator of the system is rated at 15 MW. Its contribution to the total power of the grid is 90%. The rating of the WES used in the simulation is 2 MW. It represents about 10% of the total power delivered to the loads.

After that, the simulation was repeated for the same power system model using a wind farm, a conventional synchronous generator, and load. In this study, the wind farm consists of four single WESs. Here, the synchronous generator provides 80% of the load power, while the wind farm share is

20%. The wind systems are de-loaded to maintain a certain power reserve to be utilized for frequency regulation. Due to the wake effect, the produced wind power and the reserves are not similar for all wind systems. Therefore, some wind systems may have a much higher power reserve than others. Different scenarios were performed to test the response of the wind farm using several droop rates.

**Figure 6.** Power system model with a wind farm of 4 wind turbine systems.

### *5.1. Frequency Support by Single WES*

To study the response of wind turbines to frequency deviation, several simulation-based studies were performed. The goal was to compare the responses of different droop curves for different ROCOF. The sensitivity to different droop gains was studied and compared with different control approaches.

### 5.1.1. The Response of WES to Large ROCOF

For this case study, the WES was producing its maximum power (2.0 MW). The power reserve of the WES was set to 1.0 MW (i.e., a 50% rate). First, the frequency regulation was achieved using the proposed fuzzy-logic controller. Then, the simulation was repeated using two different static droop rates (*R* = 2%, 7%). Figure 7 demonstrates the system frequency of the baseline simulation (without WES participation in frequency regulation). Figure 8 shows the frequency of the grid for the three simulation studies (fuzzy logic, *R* = 2%, 7%). The proposed fuzzy logic-based controller provides an acceptable frequency support if compared to both static droop curves.

**Figure 7.** Grid frequency of the event without wind turbine participation.

**Figure 8.** Grid frequency (large ROCOF).

The rate of dynamic droop starts at 10% and then decreases to about 3% at the beginning of the incident. After a few seconds, it reaches 2% (very fast), when the frequency drops to its minimum value as shown in Figure 9. For 7% static droop, the WES has a very slow response. On the other hand, the response of WES with 2% static droop is very fast.

**Figure 9.** Dynamic droop (large ROCOF).

As defined in the fuzzy logic, the dynamic droop controller should react very quickly when the power reserve and ROCOF are large. Consequently, the response of the WES with dynamic droop is quite similar to the one with the static droop curve of 2%. The active power of the WES and the rotation speed of the turbine's shaft during the response to frequency drop are shown in Figures 10 and 11.

**Figure 10.** Rotor speed (large ROCOF).

**Figure 11.** Wind turbine power (large ROCOF).

### 5.1.2. Response of WES to Small ROCOF

In this scenario, the WES was maintaining a reserve of 150 kW. This reserve was achieved by the controller of the rotor speed (using machine side converter). For comparison, the frequency support was provided using the proposed approach (fuzzy-logic) and two constant rate droops (i.e., *R* = 2% and 7%).

The measured frequency of the power system for the three droops (dynamic droop, *R* = 2% and 7%) is shown in Figure 12. The plot shows the proposed droop controller supports the frequency. The rate of the proposed droop controller is shown in Figure 13. The rate starts at the minimum value, which is 10%, and changes to about 5% in the beginning of the frequency drop. After that, it oscillates and returns to 10% when a new steady state value is achieved.

**Figure 13.** Dynamic droop (small ROCOF).

In this simulation, the response of the WES using constant droop of 7% is reasonable. In contrast, the response with a constant curve of 2% is quick. As can be noticed from Figure 14, the rotor speed of the WES oscillates aggressively. This high oscillation may lead to instability in the controller of the machine side converter. Also, some stresses and mechanical loading can be observed on the wind turbine. Because of the limited reserve and insignificant drop in the frequency, the droop rate of the controller has to be slow. Thus, the grid frequency can be achieved by the proposed droop controller, which in this case study is very close to the response of seven percent droop curve. The active power produced by the WES during the frequency regulation for all three studies is demonstrated in Figure 15.

**Figure 15.** Wind turbine power (small ROCOF).

### *5.2. Frequency Support by Wind Farm*

In this study, an electrical system shown in Figure 6 is simulated. The electrical grid consists of one conventional synchronous generator with its governor system, wind power plant, and a large load. For the simulation time constraint, four single WESs are considered to represent the wind farm. The power supplied to the load is distributed between the wind farm (20%) and the conventional generator (80%).

The response of every WES was observed using the proposed controller. A reserve of 2000 kW was maintained by the wind farm using a method proposed in reference [52]. The fuzzy logic-based controller was implemented to provide frequency support. Every individual WES was assigned to maintain a certain reserve that is different from others. The total power reserve was divided among all WESs as ΔPWT1 = 250 kW, ΔPWT2 = 350 kW, ΔPWT3 = 600 kW, ΔPWT4 = 800 kW.

The frequency is measured at the point as shown in Figure 16. The proposed dynamic controller provides support to the grid's frequency. The frequency goes to the minimum point (nadir) within 3 s and then it starts to return to new steady-state value. The rates of the dynamic controller for all WES are shown in Figure 17. The rates of wind turbines 1 and 2 are slower than the rates of wind turbines 3 and 4; because of the small amount of reserve available in 1 and 2. The power produced by the synchronous generator and the wind farm is shown in Figures 18 and 19. The power produced by each WES is demonstrated in Figure 18. The power of wind turbines 3 and 4 changes rapidly compared to the power of wind turbines 1 and 2 as shown in Figure 19. Also, the rotational speed of each turbine is shown in Figure 20. In this study, the controller of the rotor speed and the pitch angle actuator are activated, and the WES is tracking the reference signal given by the fuzzy logic controller as demonstrated in Figure 21.

**Figure 18.** Power: grid, synchronous generator, and wind farm.

**Figure 21.** Pitch angle (wind farm).
